This mixed-methods study explores whether undergraduates in a multilingual, multicultural university -- and more specifically in a multi-dimensionally internationalised classroom -- manifest transcultural competence when starting university studies. The article precisely focuses on the role of intercultural friendships and personal and family plurilingualism in the construction of an identity that reveals such competence, namely, a transcultural identity. Data include profile and transcultural competence questionnaires as well as interviews and classroom observations. Descriptive statistics and regression analyses show that first-year undergraduates in such a university display transcultural competence at the start of their studies, but more so students with intercultural friendships, personal or family plurilingualism, or belonging to a multi-dimensionally internationalised classroom. Qualitative data document that this educational context may trigger affordances for diversified plurilingual intercultural interactions in which transcultural competence may manifest in the form of a complex transcultural "twenty-first-century youth identity" that is linked to sensitivities and attitudes valuing heritage as well as a transnational way of life.